This article addresses historical consistency in Iris analyses.
Overview
Deformation estimates derived from synthetic aperture radar (SAR) data can change with successive analyses of the SAR data. These inconsistencies are due to the nature of the algorithms used to estimate deformation and due to unexpected changes in surface properties. These inconsistencies are referred to as “the history problem”. Iris includes a means to view the size of these inconsistencies with the aim of helping users interpret the deformation results derived from SAR data.
Content
InSAR-based deformation and the history problem
Iris features to assess the history problem
InSAR-based deformation and the history problem
A deformation time series derived from SAR data has an important property. The deformation reported at a specific point in space and time depends on the input SAR data at every point in space and time. This dependence occurs in several places.
SAR data is noisy, and the first step in the Iris deformation pipeline is to remove the noise. Given noisy data at times A, B and C, the estimates for the noise ensure that the change from A to B combined with the change from B to C should be the same as the change from A to C. Essentially the algorithms requires that, after removing noise, the data should be temporally consistent. Note that this approach to removing noise at time B depends on the input data at A, B and C, not just B. Points are included in the SAR analysis if the estimated noise is small.
Once there is a temporally consistent set of data, the Iris deformation pipeline estimates spatially consistent data. To do this Iris creates a spatial network connecting neighboring points, where the links contain estimated differences between neighboring points. The data along each link are adjusted so that the deformation difference between two points is the same regardless of path through the network between the points. One can think of this as spatially integrating the changes along different paths through the network to arrive at point values.
Fig 1: Optical data overlaid with “good” SAR points in red, where neighbors are connected by links in blue.
Figure 1 provides an example of the network used to verify spatial consistency. The nature of SAR data leaves an ambiguity in the difference in each blue link. Resolving these ambiguities in a consistent way (known as unwrapping) is a global spatial operation.
At this point the Iris pipeline has temporally and spatially consistent data. The final step is to remove any systematic contributions to the data. The main contributions are atmospheric effects and orbit path variation. These contributions are inferred based on spatial and temporal trends. In this regard, the estimates for these contributions are very much like curve fitting, which depends on all available data.
Iris always operates on a time window of at least a year of data. With every new SAR collection, Iris shifts this time window forward in time to include the most recent collection. The year long time window increases Iris’ ability to de-noise data, and to identify and remove systematic contributions.
Fig 2: Here is an example of the history problem for four different year-long analyses. The top shows the deformation histories at the green marker in the lower plot, which contains “good” points colored by cumulative deformation for the first of the four analyses.
Figure 2 shows an example where four year-long analyses exhibited different estimated deformation during the first half of 2024. The causes of this historical inconsistency can include proximity to noisy points, steep terrain, and changes in surface property.
Iris features to assess the history problem
As of January 2025, Iris analyses include ancillary data that shows the spread of historical results. For analyses that include these ancillary data, the layer drop down will include “Historical LOS”, or similar for east-vertical analyses.
Selecting “Plot STD” will show time series plots like the one below.
Fig 3: Time series plot for historical data.
Figure 3 shows an example of the historical time series data. The key elements of this plot are as follows:
- The data plotted in blue is the mean of the historical deformation, this is taken over the ten most recent available analyses of this site, including the most recent one.
- The blue error bars are the standard deviation of the ten most recent analyses.
- The data plotted in red is the deformation for the most recent analysis.
- The red error bars are the uncertainty estimates from the Iris pipeline.
All historical analyses are normalized to track deformation since the first date in the most recent analysis. For this reason, historical will always have mean zero at the first date displayed.
Note also that only the most recent analysis provides data for the most recent date, and only the most recent two analyses provide data for the second to most recent date. For this reason, at the most recent date, the mean is computed over a single element, specifically the deformation from the most recent analysis. Similarly, the historical standard deviation at the most recent date is zero.
These data allow the user to see how much a result may be impacted by the historical inconsistencies. This would be indicated by either a sharp difference in the historical mean (the blue curve) from the most recent analysis (the red curve), or large error bars associated with the historical data.